Chapter 4.5, Problem 8E

To determine

If the model fits the given data in the table accurately.

Answer to Problem 8E

The model is not a good fit for the data values.

Explanation of Solution

Given information: Table of data containing values of $x$ and $y$ is given and equation of model is $y=-0.5x-2$ .

Calculation:

Calculating the residuals using the model and given data and arranging the results in a table,

  $\begin{array}{llll}x\hfill & y\hfill & y(\mathrm{mod}el)\hfill & \mathrm{Re}siduals\hfill \\ 4\hfill & -1\hfill & -4\hfill & 3\hfill \\ 6\hfill & -3\hfill & -5\hfill & 2\hfill \\ 8\hfill & -6\hfill & -6\hfill & 0\hfill \\ 10\hfill & -8\hfill & -7\hfill & -1\hfill \\ 12\hfill & -10\hfill & -8\hfill & -2\hfill \\ 14\hfill & -10\hfill & -9\hfill & -1\hfill \\ 16\hfill & -10\hfill & -10\hfill & 0\hfill \\ 18\hfill & -9\hfill & -11\hfill & 2\hfill \\ 20\hfill & -9\hfill & -12\hfill & 3\hfill \end{array}$

Graph:

Making the scatter plot from the data,

  

Interpretation: As points are not evenly dispersed above and below the horizontal axis and residuals would not sum to a number near about $0$ . The points are forming a V-shaped pattern, the equation $y=-0.5x-2$ doesn’t model the data values accurately.

Thus, the model is not a good fit for the data values.